From (1) and (3), it follows that e0 has a cause e1, which in turn has a cause e2, and so on, in an infinite regress.

From (2) we know that there can be no infinite regress, which contradicts (4).

Therefore, at least one of the premises must be false.

If we reject premise 1, that every event has a cause, then there must be at least one uncaused cause, which can be called "God".

Why call it God?

Even if we accept the argument from first cause, the conclusion is still problematic: the word "God" carries a lot of undesirable cultural baggage, denoting an intelligent being. If the ultimate cause of our universe turns out to be, say, a random vacuum fluctuation, then that would be "God" by Aquinas's definition, but to call this phenomenon "God" would be misleading. It also can be noted that if for some reason there did have to be a first cause, we currently do not currently know what which leads to the "God of the gaps" idea.